Theme Essential Question: How do we use a system of equations to model real world situations that have multi-constraints to simulate relationships?
Essential Questions: How are systems of equations represented and interpreted algebraically?
Standards Analyze and solve pairs of simultaneous linear equations.
8. EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
8. EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
Objectives The student will use the substitution method to solve and interpret the solution to a system of linear equations.
Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team If a student is struggling with the level of independent working required from the Cell Phone Plan/ Car Comparison Project, we have provided a more structured project from NCTM, Supply and Demand. It is the teacher’s discretion to modify as needed.
Assessment Product http://mwstrange.com/Systems%20of%20Linear%20Equations%20Group%20Project.pdf In this project the students will be choosing between two real life situations and then using systems of linear equations to decide what to buy. Please be advised computer access will be advantageous. Week 1: Teacher introduction to the project and rubric. Week 2: Students thoroughly exploring and selecting their project. Week 3: Students will conduct research and apply a graphical solution to their project (manually or using technology). Week 4: Students will support their solution by using the substitution method and/or the elimination method to their project. Week 5: Students will analyze their solution, complete their project, and conduct presentations.
What is the process to algebraically solve a system of equations by substitution method?
What algebraic solution indicates the outcomes are parallel lines, interesecting lines, or lines that coincide?
Observable Student Behaviors
The student can solve and interpret a solution of a system of linear equations by the substitution method.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Suggested Activities [see Legend to highlight MCO and HYS]
Houghton Mifflin OnCore Mathematics Middle School Grade 8
Unit 3.4, p. 79-82
ABC Mastering the Common Core in Mathematics Chapter 6.3, p. 79-80
Gizmo Lessons
8.EE.8b
Solving Linear Systems by Graphing
Compare a system of equations in standard form or in slope‑intercept form to its graph. Examine the graph and table of values. Determine the solutions to the system.
Systems of Linear Equations - Activity A
Solve a system of linear equations by graphing and finding the intersection of the lines of the equations. Create a system of equations, examine its graph, matrix, and table of values, and determine the solution of the system.
8.EE.8c
Modeling Linear Systems - Activity A
Experiment with a system of two lines representing a cat‑and‑mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real‑world meaning to slope, y‑intercept, and the intersection of lines.
Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
Content: Solving Systems Algebraically (Substitution)
Dates: 4/22-4/26
Theme Essential Question:
How do we use a system of equations to model real world situations that have multi-constraints to simulate relationships?
Essential Questions:
How are systems of equations represented and interpreted algebraically?
Standards
Analyze and solve pairs of simultaneous linear equations.
Objectives
The student will use the substitution method to solve and interpret the solution to a system of linear equations.
Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team
If a student is struggling with the level of independent working required from the Cell Phone Plan/ Car Comparison Project, we have provided a more structured project from NCTM, Supply and Demand. It is the teacher’s discretion to modify as needed.
Assessment
Product
http://mwstrange.com/Systems%20of%20Linear%20Equations%20Group%20Project.pdf
In this project the students will be choosing between two real life situations and then using systems of linear equations to decide what to buy. Please be advised computer access will be advantageous.
Week 1: Teacher introduction to the project and rubric.
Week 2: Students thoroughly exploring and selecting their project.
Week 3: Students will conduct research and apply a graphical solution to their project (manually or using technology).
Week 4: Students will support their solution by using the substitution method and/or the elimination method to their project.
Week 5: Students will analyze their solution, complete their project, and conduct presentations.
Additional Option
Supply and Demand Activity from NCTM
http://inside.mines.edu/~preitz/SupplyDemand-AS-Applications_OLD.pdf (Student Worksheet)
http://illuminations.nctm.org/lessons/9-12/Supply/SupplyDemand-AS-ApplicationsKEY_OLD.pdf (Solution)
This activity focuses on having students create and solve a system of linear equations in a real-world setting. By solving the system, students will find the equilibrium point for supply and demand. Students should be familiar with finding linear equations from two points or slope and y-intercept. This lesson was adapted from the October 1991 edition of Mathematics Teacher.
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary
Slope-intercept form, solution, outcome
Suggested Activities [see Legend to highlight MCO and HYS]
- Houghton Mifflin OnCore Mathematics Middle School Grade 8
Unit 3.4, p. 79-82- ABC Mastering the Common Core in Mathematics Chapter 6.3, p. 79-80
Gizmo Lessons- 8.EE.8b
- Solving Linear Systems by Graphing
- Compare a system of equations in standard form or in slope‑intercept form to its graph. Examine the graph and table of values. Determine the solutions to the system.
- Systems of Linear Equations - Activity A
- Solve a system of linear equations by graphing and finding the intersection of the lines of the equations. Create a system of equations, examine its graph, matrix, and table of values, and determine the solution of the system.
- 8.EE.8c
- Modeling Linear Systems - Activity A
- Experiment with a system of two lines representing a cat‑and‑mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real‑world meaning to slope, y‑intercept, and the intersection of lines.
- Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
- 8.EE.8 Activity 1 p. 180, Activity 2 p. 181
- Glencoe Pre-Algebra- p. 414-418, p. 428
- Glencoe Algebra 1- p. 382-386
- Highly Recommended:
http://illustrativemathematics.org/illustrations/469 (G.8)http://illustrativemathematics.org/illustrations/472 (G.8)
http://illustrativemathematics.org/illustrations/554 (G.8)
http://illustrativemathematics.org/illustrations/73 (G.8)The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Diverse Learners
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Lesson Plan in Word Format (Click Cancel if asked to Log In)Resources
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- Smartboard Resource Website Smartboard lesson search engine
- 8. EE.8b System of Equations
A real life problem is used for a cue set and a backdrop for teaching how to solve a system of equations graphically.- 8. EE.8b System of Linear Equations and Linear Inequalities (Question Set)
These questions test the ability to understand and solve linear equations and linear inequalities.- 8. EE.8c Solving Problems Involving Algebraic Techniques (Question Set)
Solving Problems Involving Algebraic Techniques (Question set)Websites
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